Add Shower to 1/2 Bath / Laundry Room

I would like to expand my half-bath/laundry room to include a shower stall. I have sepate drain lines for the toilet, sink, and washer. Would it be possible to tie in the shower drain into one of the existing drains? Or do I need to run a new drain and vent? My initial thought is to use the existing washer drain and tie the washer in upstream.

its all about what the Code will let you do in your jurisdiction. I can think of two things that Code will cover.
- 1. Drainage Fixture Units (DFU) is the big thing, and that relates to the size of your drain.
- 2. Whether the washer drain has to be isolated from bathoom drains. In my building, I am allowed to connect only two specific things {a wash basin and a HW tank} to the washer drain but not the fixtures of a bathroom {tub, shower, sink, toilet}.

Let us all know a little bit more and hope that you get good advice after that. I'm not a plumber.